WAEC Mathematics 2017 Theory — Question 18

Question 18 of 25 from the West African Examinations Council (WAEC) Mathematics 2017 Theory paper, with the correct answer and a full explanation.

10(a) Given that sin x=5/13, 0°≤x<90°, find (cos x - 2 sin x)/(2 tan x)

Model answer

Using a right-angled triangle with opposite=5, hypotenuse=13, by Pythagoras' theorem, adjacent=12. So cos x=12/13, tan x=5/12. Substituting: (12/13 - 2(5/13))/(2(5/12)) = (12/13-10/13)/(5/6) = (2/13)/(5/6) = (2/13)x(6/5) = 12/65.

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